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Sharing the costs of cleaning a river: the Upstream Responsibility rule

Author

Listed:
  • Jorge Alcalde-Unzu

    () (Departamento de Economía-UPNA)

  • María Gómez-Rúa

    () (Department of Statistics and Operations Research-Universidad de Vigo)

  • Elena Molis

    () (Department of Economics-Universidad de Granada)

Abstract

The cleaning up of waste present in transboundary rivers, which requires the cooperation of diferent authorities, is a problematic issue, especially when responsibility for the discharge of the waste is not well-defined. Following Ni and Wang [12] we assume that a river is a segment divided into several regions from upstream to downstream. We show that when the transfer rate of the waste is unknown, the clean-up cost vector provides useful information for estimating some limits in regard to the responsibility of each region. We propose a cost allocation rule, the Upstream Responsibility rule, which takes into account these limits in distributing costs "fairly" and we provide an axiomatic characterization of this rule via certain properties based on basic ideas concerning the responsibility of regions.

Suggested Citation

  • Jorge Alcalde-Unzu & María Gómez-Rúa & Elena Molis, 2013. "Sharing the costs of cleaning a river: the Upstream Responsibility rule," Documentos de Trabajo - Lan Gaiak Departamento de Economía - Universidad Pública de Navarra 1301, Departamento de Economía - Universidad Pública de Navarra.
  • Handle: RePEc:nav:ecupna:1301
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    References listed on IDEAS

    as
    1. Wang, Yuntong, 2011. "Trading water along a river," Mathematical Social Sciences, Elsevier, vol. 61(2), pages 124-130, March.
    2. Ambec, Stefan & Ehlers, Lars, 2008. "Sharing a river among satiable agents," Games and Economic Behavior, Elsevier, vol. 64(1), pages 35-50, September.
    3. Ambec, Stefan & Sprumont, Yves, 2002. "Sharing a River," Journal of Economic Theory, Elsevier, vol. 107(2), pages 453-462, December.
    4. Yann Rébillé & Lionel Richefort, 2012. "Sharing Water from many Rivers," Working Papers hal-00678997, HAL.
    5. Anna Khmelnitskaya, 2010. "Values for rooted-tree and sink-tree digraph games and sharing a river," Theory and Decision, Springer, vol. 69(4), pages 657-669, October.
    6. Parrachino, Irene & Dinar, Ariel & Patrone, Fioravante, 2006. "Cooperative game theory and its application to natural, environmental, and water resource issues : 3. application to water resources," Policy Research Working Paper Series 4074, The World Bank.
    7. Barret, Scott & DEC, 1994. "Conflict and cooperation in managing international water resources," Policy Research Working Paper Series 1303, The World Bank.
    8. Beard, Rodney, 2011. "The river sharing problem: A review of the technical literature for policy economists," MPRA Paper 34382, University Library of Munich, Germany.
    9. Segerson, Kathleen, 1988. "Uncertainty and incentives for nonpoint pollution control," Journal of Environmental Economics and Management, Elsevier, vol. 15(1), pages 87-98, March.
    10. Gerard van der Laan & Nigel Moes, 2012. "Transboundary Externalities and Property Rights: An International River Pollution Model," Tinbergen Institute Discussion Papers 12-006/1, Tinbergen Institute.
    11. van den Brink, René & van der Laan, Gerard & Moes, Nigel, 2012. "Fair agreements for sharing international rivers with multiple springs and externalities," Journal of Environmental Economics and Management, Elsevier, vol. 63(3), pages 388-403.
    12. repec:wsi:igtrxx:v:15:y:2013:i:03:n:s0219198913400161 is not listed on IDEAS
    13. María Gómez-Rúa, 2013. "Sharing a polluted river through environmental taxes," SERIEs: Journal of the Spanish Economic Association, Springer;Spanish Economic Association, vol. 4(2), pages 137-153, June.
    14. Baomin Dong & Debing Ni & Yuntong Wang, 2012. "Sharing a Polluted River Network," Environmental & Resource Economics, Springer;European Association of Environmental and Resource Economists, vol. 53(3), pages 367-387, November.
    15. Sylvain Beal & Amandine Ghintran & Eric Remila & Philippe Solal, 2013. "The River Sharing Problem: A Survey," International Game Theory Review (IGTR), World Scientific Publishing Co. Pte. Ltd., vol. 15(03), pages 1-19.
    16. S. C. Littlechild & G. Owen, 1973. "A Simple Expression for the Shapley Value in a Special Case," Management Science, INFORMS, vol. 20(3), pages 370-372, November.
    17. Ni, Debing & Wang, Yuntong, 2007. "Sharing a polluted river," Games and Economic Behavior, Elsevier, vol. 60(1), pages 176-186, July.
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    Citations

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    Cited by:

    1. René van den Brink & Simin He & Jia-Ping Huang, 2015. "Polluted River Problems and Games with a Permission Structure," Tinbergen Institute Discussion Papers 15-108/II, Tinbergen Institute.
    2. Bergantiños, Gustavo & Vidal-Puga, Juan, 2016. "One-way and two-way cost allocation in hub network problems," MPRA Paper 74875, University Library of Munich, Germany.
    3. Jorge Alcalde-Unzu & Maria Gomez-Rua & Elena Molis, 2018. "Allocating the costs of cleaning a river; estimating responsibilities versus incentive compatibility," ThE Papers 18/02, Department of Economic Theory and Economic History of the University of Granada..
    4. Takayuki Oishi & Gerard van der Laan & René van den Brink, 2018. "The Tort Law and the Nucleolus for Generalized Joint Liability Problems," Working Papers 37, Meisei University, School of Economics.
    5. repec:eee:gamebe:v:108:y:2018:i:c:p:182-205 is not listed on IDEAS

    More about this item

    Keywords

    Cost allocation; waste river; responsibility; characterizations;

    JEL classification:

    • C71 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Cooperative Games
    • D61 - Microeconomics - - Welfare Economics - - - Allocative Efficiency; Cost-Benefit Analysis

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